The Spartak Moscow winger has been ruled out of the matches against Sweden and Austria because of a knee problem.
McGeady was named in boss Giovanni Trapattoni's provisional 29-man squad but was a notable absentee when the Italian trimmed his list to 23 players.
The Football Association of Ireland confirmed injuries had forced the withdrawals of McGeady, Hull defender Paul McShane and Norwich winger Anthony Pilkington.
The Republic face Sweden in Stockholm next Friday, before taking on Austria in Dublin four days later.
McGeady missed Spartak's Russian Premier League clash on Saturday, with McShane (ankle) and Pilkington (hamstring) also sidelined.
Meanwhile, Trapattoni has relegated West Ham full-back Joey O'Brien, Reading centre-back Alex Pearce and Wolves pair Stephen Ward and Kevin Doyle to standby duty.
But Millwall striker Andy Keogh, who was not in the original squad, has received a call-up.
Trapattoni said: "As a manager, I am sometimes faced with some very tough decisions, but I feel that the squad I have chosen will get us the results we need from these two qualifiers.
"I have not made these choices lightly and will continue to monitor each player's progress ahead of our next challenges in May and June."